Diffractive optical element and optical device

ABSTRACT

In a diffractive optical element, a first optical member and a second optical member are stacked, and a diffraction grating is formed at an interface between the first and second optical members. The diffractive optical element is configured so that the followings fall within a predetermined range: an inter-material gradient which is a ratio of an amount of change in reference refractive indexes between the first optical member and the second optical member, to an amount of change in principal dispersions between the first optical member and the second optical member; and a blaze wavelength of the diffraction grating.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Japanese Patent Application No.2009-298067 filed on Dec. 28, 2009, the disclosure of which includingthe specification, the drawings, and the claims is hereby incorporatedby reference in its entirety.

BACKGROUND

The present disclosure relates to a diffractive optical element in whichtwo optical members are stacked, and a diffraction grating is formed atan interface between the two optical members; and to an optical deviceincluding the diffractive optical element.

A diffractive optical element has been known, in which a plurality ofoptical members are stacked, and a relief pattern is formed at aninterface between the optical members.

In a diffractive optical element described in, e.g., Japanese PatentPublication No. 09-127321, a relatively low-refractive high-dispersiveoptical material, and a relatively high-refractive low-dispersiveoptical material are stacked, and a diffraction grating having asaw-tooth cross-sectional shape is formed at an interface between theoptical materials. More specifically, the diffractive optical element isconfigured so that a refractive index difference between the two opticalmaterials is smaller for light having a shorter wavelength, and islarger for light having a longer wavelength. In a diffractive opticalelement described in Japanese Patent Publication No. 2009-217139, acombination of such optical materials reduces wavelength dependency ofdiffraction efficiency.

SUMMARY

However, even if two optical materials are selected under conditionsdescribed in Japanese Patent Publication No. 09-127321, the wavelengthdependency of the diffraction efficiency cannot be sufficiently reduced.That is, there is room for improvement in reducing the wavelengthdependency of the diffraction efficiency.

The present disclosure has been made in view of the foregoing, and it isan object of the present disclosure to reduce the wavelength dependencyof the diffraction efficiency in the diffractive optical element inwhich the two optical materials are stacked, and the diffraction gratingis formed at the interface between the two optical materials.

The present disclosure is to reduce the wavelength dependency of thediffraction efficiency considering a blaze wavelength in addition to arefractive index of the optical material. Specifically, the presentdisclosure is intended for a diffractive optical element including firstand second optical members which are stacked, and which have adiffraction grating formed at an interface between the first and secondoptical members. In addition, in the diffractive optical element,expressions (1)-(3) or (4)-(6) are satisfied:0.400≦λ_(b)≦0.460  (1)M≧1339242229.625×λ_(b) ⁶−3467101052.6675×λ_(b) ⁵+3739417158.03949×λ_(b)⁴−2150706261.50666×λ_(b) ³+695699517.122797×λ_(b)²−120005677.292515×λ_(b)+8624042.63627238  (2)M≦−1332094191.9375×λ_(b) ⁶+3449257434.95906×λ_(b)⁵−3720886459.39374×λ_(b) ⁴+2140458094.5947×λ_(b)³−692516647.829495×λ_(b) ²+119479540.773725×λ_(b)−8587922.98149309  (3)0.560≦λ_(b)≦0.650  (4)M≧79855185.5390625×λ_(b) ⁶−291350087.799711×λ_(b)⁵+442815879.530274×λ_(b) ⁴−358873164.839002×λ_(b)³+163567486.506001×λ_(b) ²−39753252.4920047×λ_(b)+4024975.0978217  (5)M≦−82526017.6289062×λ_(b) ⁶+301239002.375121×λ_(b)⁵−458051447.988191×λ_(b) ⁴+371372898.921825×λ_(b)³−169325896.092434×λ_(b) ²+41165269.8970695×λ_(b)−4168933.51144255  (6)

where “λ_(b)” is a blaze wavelength (μm);M={n₁(λ₂)−n₂(λ₂)}/{n₁(λ₁)−n₁(λ₃)−n₂(λ₁)+n₂(λ₃)}; “n₁(λ)” is a refractiveindex of the first optical member for incident light having a wavelengthλ; “n₂(λ)” is a refractive index of the second optical member for theincident light having the wavelength λ; “λ₁” is 0.486133 μm; “λ₂” is0.587562 μm; and “λ₃” is 0.656273 μm.

In addition, another aspect of the invention is intended for adiffractive optical member including first and second optical memberswhich are stacked, and which have a diffraction grating formed at aninterface between the first and second optical members. In thediffractive optical element, expressions (19)-(23) are satisfieddepending on a blaze wavelength (μm):

(i) when 0.402≦λ_(b)<0.423,M≧−5.67  (19)M≦−2059169.7421875×λ_(b) ⁶+5816357.49453125×λ_(b)⁵−6788300.15627441×λ_(b) ⁴+4193835.50001671×λ_(b)³−1448014.62341355×λ_(b) ²+265253.074154754×λ_(b)−20174.8108751328  (20)

(ii) when 0.423≦λ_(b)<0.664,−5.67≦M≦−4.70  (21)

(iii) when 0.664≦λ_(b)≦0.695,M≧−1737676.76663208×λ_(b) ⁶+6606429.15555359×λ_(b)⁵−10426872.1241855×λ_(b) ⁴+8742622.74935995×λ_(b)³−4106195.43419261×λ_(b) ²+1024012.6733048×λ_(b)−105911.832822947  (22)M≦−4.70  (23)

where M={n₁(λ₂)−n₂(λ₂)}/{n₁(λ₁)−n₁(λ₃)−n₂(λ₁)+n₂(λ₃)}; “n₁(λ)” is arefractive index of the first optical member for incident light having awavelength λ; “n₂(λ)” is a refractive index of the second optical memberfor the incident light having the wavelength λ; “λ₁” is 0.486133 μm;“λ₂” is 0.587562 μm; and “λ₃” is 0.656273 μm.

According to the present disclosure, the wavelength dependency of thediffraction efficiency across an entire visible wavelength range can bereduced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a camera to which an interchangeable lensof an embodiment of the present disclosure is attached.

FIG. 2 is a schematic cross-sectional view of a diffractive opticalelement.

FIG. 3 is a schematic diagram of a diffraction grating.

FIG. 4 is a graph illustrating a relationship of an average diffractionefficiency across visible wavelength with an inter-material gradient Mand a blaze wavelength λ_(b)), and is a graph illustrating a preferablerange of the inter-material gradient M.

FIG. 5 is a graph illustrating the relationship of the averagediffraction efficiency across visible wavelength with the inter-materialgradient M and the blaze wavelength λ_(b), and is a graph illustratingpreferable ranges of the inter-material gradient M and the blazewavelength λ_(b).

FIG. 6 is a graph illustrating a diffraction efficiency in a visiblewavelength range, which corresponds to Table 1.

FIG. 7 is a graph illustrating the relationship of the averagediffraction efficiency across visible wavelength with the inter-materialgradient M and the blaze wavelength λ_(b), and is a graph illustratingmore preferable ranges of the inter-material gradient M and the blazewavelength λ_(b).

FIG. 8 is a graph illustrating the relationship of the averagediffraction efficiency across visible wavelength with the inter-materialgradient M and the blaze wavelength λ_(b)), and is a graph illustratingfurther preferable ranges of the inter-material gradient M and the blazewavelength λ_(b)).

FIG. 9 is a graph illustrating the relationship of the averagediffraction efficiency across visible wavelength with the inter-materialgradient M and the blaze wavelength λ_(b)), and is a graph illustratingother preferable ranges of the inter-material gradient M and the blazewavelength λ_(b).

FIG. 10 is a graph illustrating the diffraction efficiency in thevisible wavelength range, which corresponds to Table 3.

FIG. 11 is a graph illustrating a relationship between a principaldispersion and a reference refractive index of optical material.

FIG. 12 is a model of a diffraction grating used for a simulation by aRCWA method.

FIG. 13 is a graph illustrating a relationship of the diffractionefficiency with an absorption coefficient α and a grating height h.

FIG. 14 is a schematic diagram for illustrating the grating height h fora non-uniform shape of the diffraction grating.

DETAILED DESCRIPTION

An embodiment of the present disclosure will be described in detailbelow with reference to the drawings.

Embodiment of the Disclosure

FIG. 1 is a schematic view of an interchangeable lens 200 with adiffractive optical element 1 illustrated as an example of the presentembodiment, and a camera 100 to which the interchangeable lens 200 isattached. FIG. 2 is a schematic cross-sectional view of the diffractiveoptical element 1.

The interchangeable lens 200 is detachable from the camera 100. Theinterchangeable lens 200 is, e.g., a telephoto zoom lens. In theinterchangeable lens 200, the diffractive optical element 1 serves as alens element in addition to a refractive lens.

The diffractive optical element 1 is formed by stacking a first opticalmember 10 and a second optical member 11 which are transparent to light.In the present embodiment, the first optical member 10 is made of resinmaterial, and the second optical member 11 is made of glass material.The first optical member 10 and the second optical member 11 are bondedtogether. A diffraction grating 13 having a saw-tooth cross-sectionalshape is formed at an interface 12 defined by a bonding surface 10 a ofthe first optical member 10 and a bonding surface 11 a of the secondoptical member 11. Optical power of the diffraction grating 13 haswavelength dependency. Thus, the diffraction grating 13 provides thesubstantially same phase difference to light having differentwavelengths, and diffracts the light having different wavelengths atdiffraction angles which are different from each other.

Specifically, a recessed first diffraction grating 14 is formed in thebonding surface 10 a of the first optical member 10, and a raised seconddiffraction grating 15 is formed in the bonding surface 11 a of thesecond optical member 11. The first diffraction grating 14 includes aplurality of recessed sections which extend in a circumferentialdirection around an optical axis of the diffractive optical element 1,and which are concentrically and regularly arranged around the opticalaxis. Each of the recessed sections has a surface which is substantiallyparallel to the optical axis, and a surface inclined toward the opticalaxis; and has a substantially triangular cross section. In addition, thesecond diffraction grating 15 includes a plurality of raised sectionswhich extend in the circumferential direction around the optical axis ofthe diffractive optical element 1, and which are concentrically andregularly arranged around the optical axis. Each of the raised sectionshas a surface which is substantially parallel to the optical axis, and asurface inclined toward the optical axis; and has a substantiallytriangular cross section. The first diffraction grating 14 and thesecond diffraction grating 15 have the same grating height and the samegrating pitch. That is, the raised sections of the second diffractiongrating 15 are fully engaged with the recessed sections of the firstdiffraction grating 14. As a result, the bonding surface 10 a of thefirst optical member 10 contacts the bonding surface 11 a of the secondoptical member 11 with no gap, thereby defining the single interface 12.The first diffraction grating 14 and the second diffraction grating 15together form the diffraction grating 13. Note, however, that a middlelayer of, e.g., air, an anti-reflective film, and an adhesive, which hasa refractive index different from those of the first diffraction grating14 and the second diffraction grating 15 may be interposed between thebonding surface 10 a and the bonding surface 11 a as long as the bondingsurface 10 a and the bonding surface 11 a are substantially parallel toeach other.

Chamfering or R-chamfering may be applied to a valley of the recessedsection of the first diffraction grating 14, and to a ridge of theraised section of the second diffraction grating 15 (i.e., a peak of thetriangle as viewed in cross section). The inclined surface of therecessed section of the first diffraction grating 14, and the inclinedsurface of the raised section of the second diffraction grating 15 maybe curved so as to define an aspherical or spherical surface.

A surface 10 b of the first optical member 10 on a side opposite to thebonding surface 10 a, and a surface 11 b of the second optical member 11on a side opposite to the bonding surface 11 a are formed into flatsurfaces parallel to each other. As illustrated in FIG. 1, e.g., lightentering the diffractive optical element 1 from the first optical member10 side is diffracted by the diffraction grating 13 to exit to thesecond optical member 11 side. Note that the surface 10 b of the firstoptical member 10 and the surface 11 b of the second optical member 11may not be parallel to each other.

The diffractive optical element 1 configured as described abovesatisfies an expression (12):−6.30≦M≦−4.55  (12)

where M={n₁(λ₂)−n₂(λ₂)}/{n₁(λ₁)−n₁(λ₃)−n₂(λ₁)+n₂(λ₃)}; “n₁(λ)”represents a refractive index of the first optical member for incidentlight having a wavelength λ; “n₂(λ)” represents a refractive index ofthe second optical member for the incident light having the wavelengthλ; “λ₁” is 0.486133 μm; “λ₂” is 0.587562 μm; and “λ₃” is 0.656273 μm.

Specifically, in the expression (12), “λ₁” is an F-line wavelength; “λ₂”is a d-line wavelength; and “λ₃” is a C-line wavelength. That is, anumerator of the fraction representing “M” is a difference between areference refractive index (n₁(λ₂)) of the first optical member 10 and areference refractive index (n₂(λ₂)) of the second optical member 11; anda denominator is a difference between a principal dispersion(n₁(λ₁)−n₁(λ₃)) of the first optical member 10 and a principaldispersion (n₂(λ₁)−n₂(λ₃)) of the second optical member 11. That is, “M”represents a ratio of an amount of change (difference) in the referencerefractive indexes between the first optical member 10 and the secondoptical member 11, to an amount of change (difference) in the principaldispersions between the first optical member 10 and the second opticalmember 11. In the specification of the present disclosure, “M” isreferred to as an “inter-material gradient.”

Wavelength dependency of diffraction efficiency of the diffractiveoptical element 1 is changed depending on the inter-material gradient M.The first and second optical members 10 and 11 are selected so that theexpression (12) is satisfied, and then the first and second opticalmembers 10 and 11 are used to produce the diffractive optical element 1.Thus, the diffraction efficiency of the diffractive optical element 1can be uniformly enhanced across an entire visible wavelength range(range in which a wavelength is 0.400 μm-0.700 μm). That is, thewavelength dependency of the diffraction efficiency across the entirevisible wavelength range can be reduced, and an average value of thediffraction efficiency across the entire visible wavelength range(hereinafter referred to as an “average diffraction efficiency acrossvisible wavelength”) can be improved.

Further, the diffractive optical element 1 satisfies expressions (1)-(3)or (4)-(6):0.400≦λ_(b)≦0.460  (1)M≧1339242229.625×λ_(b) ⁶−3467101052.6675×λ_(b) ⁵+3739417158.03949×λ_(b)⁴−2150706261.50666×λ_(b) ³+695699517.122797×λ_(b)²−120005677.292515×λ_(b)+8624042.63627238  (2)M≦−1332094191.9375×λ_(b) ⁶+3449257434.95906×λ_(b)⁵−3720886459.39374×λ_(b) ⁴+2140458094.5947×λ_(b)³−692516647.829495×λ_(b) ²+119479540.773725×λ_(b)−8587922.98149309  (3)0.560≦λ_(b)≦0.650  (4)M≧79855185.5390625×λ_(b) ⁶−291350087.799711×λ_(b)⁵+442815879.530274×λ_(b) ⁴−358873164.839002×λ_(b)³+163567486.506001×λ_(b) ²−39753252.4920047×λ_(b)+4024975.0978217  (5)M≦−82526017.6289062×λ_(b) ⁶+301239002.375121×λ_(b)⁵−458051447.988191×λ_(b) ⁴+371372898.921825×λ_(b)³−169325896.092434×λ_(b) ²+41165269.8970695×λ_(b)−4168933.51144255  (6)

where “λ_(b)” is a blaze wavelength (μm).

The wavelength dependency of the diffraction efficiency of thediffractive optical element 1 is also changed depending on the blazewavelength λ_(b). That is, the blaze wavelength λ_(b) and the first andsecond optical members 10 and 11 which satisfy the expressions (1)-(3)or (4)-(6) are selected, thereby further improving the averagediffraction efficiency across visible wavelength in the diffractiveoptical element 1. Consequently, the wavelength dependency of thediffraction efficiency across the entire visible wavelength range can befurther reduced. Specifically, the average diffraction efficiency acrossvisible wavelength can be greater than or equal to 99%.

More preferably, the diffractive optical element 1 satisfies expressions(7)-(9) or (10)-(12):0.414≦λ_(b)≦0.450  (7)M≧8640558390×λ_(b) ⁶−22380686760.9125×λ_(b)⁵+24152666332.3616×λ_(b)−13900381865.2731×λ_(b) ³+4499685153.88293×λ_(b)²−776796861.97245×λ_(b)+55871807.7607997  (8)M≦−10194570607.5×λ_(b) ⁶+26421929920.0925×λ_(b) ⁵−28531440313.7911×λ_(b)⁴+16430708380.9751×λ_(b) ³−5322137506.01958×λ_(b)²+919367999.430877×λ_(b)−66169280.3167743  (9)0.576≦λ_(b)≦0.638  (10)M≧414967120.90625×λ_(b) ⁶−1512185155.554×λ_(b) ⁵+2295832124.5403×λ_(b)⁴−1858788442.14493×λ_(b) ³+846446107.028953×λ_(b)²−205553837.085777×λ_(b)+20796969.7061844  (11)M≦−415113085.03125×λ_(b) ⁶+1512854887.23366×λ_(b)⁵−2297046202.65628×λ_(b) ⁴+1859918525.18878×λ_(b)³−847020476.777119×λ_(b) ²+205705688.874443×λ_(b)−20813340.0724713  (12)

As described above, the blaze wavelength λ_(b) and the first and secondoptical members 10 and 11 which satisfy the expressions (7)-(9) or(10)-(12) are selected, thereby further improving the averagediffraction efficiency across visible wavelength in the diffractiveoptical element 1. Consequently, the wavelength dependency of thediffraction efficiency across the entire visible wavelength range can befurther reduced. Specifically, the average diffraction efficiency acrossvisible wavelength can be greater than or equal to 99.15%.

The diffractive optical element 1 preferably satisfies expressions(13)-(15) or (16)-(18):0.417≦λ_(b)≦0.447  (13)M≧30852412488×λ_(b) ⁶−79922201016.868×λ_(b) ⁵+86260883694.3531×λ_(b)⁴−49652199810.7073×λ_(b) ³+16075519544.8254×λ_(b)²−2775681903.96431×λ_(b)+199683678.257006  (14)M≦−30584648780×λ_(b) ⁶+79226520575.83×λ_(b) ⁵−85507821323.3087×λ_(b)⁴+49217462978.353×λ₆ ³−15934356981.3252×λ_(b)²+2751237292.99331×λ_(b)−197920088.494362  (15)0.581≦λ_(b)≦0.632  (16)M≧1306900213.875×λ_(b) ⁶−4761329435.24312×λ_(b) ⁵+7227224601.18296×λ_(b)⁴−5850360432.19395×λ_(b) ³+2663701689.21584×λ_(b)²−646780698.688165×λ_(b)+65431590.8897632  (17)M≦−1286672013.625×λ_(b) ⁶+4687809955.26×λ_(b) ⁵−7115891461.56486×λ_(b)⁴+5760442316.00334×λ_(b) ³−2622849972.06735×λ_(b)²+636881343.787066×λ_(b)−64431960.7758904  (18)

As described above, the blaze wavelength λ_(b) and the first and secondoptical members 10 and 11 which satisfy the expressions (13)-(15) or(16)-(18) are selected, thereby further improving the averagediffraction efficiency across visible wavelength in the diffractiveoptical element 1. Consequently, the wavelength dependency of thediffraction efficiency across the entire visible wavelength range can befurther reduced. Specifically, the average diffraction efficiency acrossvisible wavelength can be greater than or equal to 99.20%.

The diffractive optical element 1 may satisfy expressions (19)-(23)depending on the blaze wavelength λ_(b) (μm):

(i) when 0.402≦λ_(b)<0.423,M≧−5.67  (19)M≦−2059169.7421875×λ_(b) ⁶+5816357.49453125×λ_(b)⁵−6788300.15627441×λ_(b) ⁴+4193835.50001671×λ_(b)³−1448014.62341355×λ_(b) ²+265253.074154754×λ_(b)−20174.8108751328  (20)

(ii) when 0.423≦λ_(b)<0.664,−5.67≦M≦−4.70  (21)

(iii) when 0.664≦λ_(b)≦0.695,M≧−1737676.76663208×λ_(b) ⁶+6606429.15555359×λ_(b)⁵−10426872.1241855×λ_(b) ⁴+8742622.74935995×λ₆ ³−4106195.43419261×λ_(b)²+1024012.6733048×λ_(b)−105911.832822947  (22)M≦−4.70  (23)

The blaze wavelength λ_(b) and the first and second optical members 10and 11 are selected within a range in which the expressions (19)-(23)are satisfied, and therefore the average diffraction efficiency acrossvisible wavelength in the diffractive optical element 1 can be greaterthan or equal to 98%. Although the average diffraction efficiency acrossvisible wavelength is slightly degraded as compared to a range specifiedby the expressions (1)-(6), a range of the blaze wavelength λ_(b) to beselected can be expanded. That is, if the first and second opticalmembers 10 and 11 are properly selected (i.e., the first and secondoptical members 10 and 11 are selected so as to satisfy the expressions(19)-(23)), the blaze wavelength λ_(b) can be selected within0.402≦λ_(b)≦0.695 which is a substantially full range of the visiblewavelength range. As described above, the range of the blaze wavelengthλ_(b) to be selected can be expanded, and the average diffractionefficiency across visible wavelength can be greater than or equal to 98%even in such a case.

The diffractive optical element 1 is configured so that an absorptioncoefficient α (mm⁻¹) of the first optical member 10 and a grating heighth (μm) of the diffraction grating 13 satisfy expressions (24) and (25):α≧0.04  (24)h≦263.18×α^(−0.9454)  (25)

Within a range in which the expressions (24) and (25) are satisfied,even if material which is not optically transparent (i.e., materialhaving an absorption coefficient α of greater than or equal to 0.04mm⁻¹) is used, the high diffraction efficiency can be realized. Thus,such material can be employed as the optical material of the firstoptical member 10. Specifically, the diffraction efficiency for theblaze wavelength λ_(b) can be greater than 85%.

That is, types of material to be employed as the optical material of thediffractive optical element 1 are not infinite. Thus, when the first andsecond optical members 10 and 11 are selected so that the inter-materialgradient M falls within a predetermined range as described above, arange of material selection is considerably narrowed. However, as longas the high diffraction efficiency can be realized, a certain level ofabsorption is allowed. Specifically, since the optical materialsatisfying the expressions (24) and (25) has the high diffractionefficiency, such material can be employed as the optical material of thefirst optical member 10. Consequently, the wavelength dependency of thediffraction efficiency can be reduced, and a range of the first opticalmember 10 to be selected can be expanded.

Thus, according to the present embodiment, the diffractive opticalelement 1 is configured so that the inter-material gradient M betweenthe first and second optical members 10 and 11 satisfies the expression(12), thereby improving the average diffraction efficiency acrossvisible wavelength. Consequently, the wavelength dependency of thediffraction efficiency across the entire visible wavelength range can bereduced.

When employing the diffractive optical element 1 in an optical deviceintended for white light, such as the interchangeable lens 200, it isrequired that the diffractive optical element 1 has the high diffractionefficiency across the entire visible wavelength range. The diffractiveoptical element 1 of the present embodiment has the low wavelengthdependency of the diffraction efficiency across the entire visiblewavelength range, and therefore can be employed in the optical deviceintended for white light.

Further, the diffractive optical element 1 is configured so that theblaze wavelength λ_(b) and the inter-material gradient M between thefirst and second optical members 10 and 11 satisfy the expressions(1)-(3) or (4)-(6), thus the average diffraction efficiency acrossvisible wavelength can be greater than or equal to 99%. Consequently,the wavelength dependency of the diffraction efficiency across theentire visible wavelength range can be further reduced.

The diffractive optical element 1 is preferably configured so that theblaze wavelength λ_(b) and the inter-material gradient M between thefirst and second optical members 10 and 11 satisfy the expressions(7)-(9) or (10)-(12), thus the average diffraction efficiency acrossvisible wavelength can be greater than or equal to 99.15%. Consequently,the wavelength dependency of the diffraction efficiency across theentire visible wavelength range can be further reduced.

More preferably, the diffractive optical element 1 is configured so thatthe blaze wavelength λ_(b) and the inter-material gradient M between thefirst and second optical members 10 and 11 satisfy the expressions(13)-(15) or (16)-(18), thus the average diffraction efficiency acrossvisible wavelength can be greater than or equal to 99.20%. Consequently,the wavelength dependency of the diffraction efficiency across theentire visible wavelength range can be still further reduced.

The diffractive optical element 1 is configured so as to satisfy theexpressions (19)-(23) depending on the blaze wavelength λ_(b) (μm).Thus, the range of the blaze wavelength λ_(b) to be selected can beexpanded, and the average diffraction efficiency across visiblewavelength can be greater than or equal to 98%. Consequently, thewavelength dependency of the diffraction efficiency across the entirevisible wavelength range can be reduced.

The diffractive optical element 1 is configured so as to satisfy theexpressions (24) and (25). Thus, the high diffraction efficiency can bemaintained, and the light absorption is allowed. Consequently, a rangeof the optical material to be selected can be expanded.

EXAMPLES

Examples of the diffractive optical element will be described below.FIG. 3 is a schematic cross-sectional diagram of a diffraction grating.

First, a diffraction grating 13 illustrated in FIG. 3 is assumed. Inthis case, expressions (26) and (27) are satisfied:φ(λ)=(h/λ)×{n ₁(λ)cos θ_(m) −n ₂(λ)cos θ_(i})  (26)n ₂(λ)sin θ_(m) =n ₁(λ)sin θ_(i) +mλ/P  (27)

where “φ(λ)” represents a phase difference; “h” represents a gratingheight (μm); “λ” represents a wavelength (μm); “m” represents adiffraction order; “n₁(λ)” represents a refractive index of a firstoptical member for a wavelength λ; “n₂(λ)” represents a refractive indexof a second optical member for a wavelength λ; “θ_(i)” represents anangle of incidence (degrees); “θ_(m)” represents a m-order diffractionangle (degrees); and “P” represents a grating pitch (cycle) (μm).

The phase difference φ(λ) is used to obtain a diffraction efficiencyη_(m)(λ) of m-order diffracted light for incident light having thewavelength λ based on an expression (28):n _(m)(λ)=sin c ²(φ(λ)−m)  (28)

In order to obtain a diffraction efficiency of first-order diffractedlight for light incident in a direction parallel to an optical axis,θ_(i)=0 and m=1 are assumed. P>>λ is typically satisfied. Thus, theexpression (27) provides θ_(m)=0. Consequently, each of the expressions(26) and (28) provides:φ(λ)=(h/λ)×{n ₁(λ)−n ₂(λ)}  (29)η₁(λ)=sin c ²(φ(λ)−1)  (30)

That is, the phase difference φ(λ) for each wavelength λ of the visiblewavelength range can be obtained based on the expression (29) bychanging the wavelength λ in a visible wavelength range. Further, bysubstituting the phase difference into the expression (30), adiffraction efficiency η₁(λ) of first-order diffracted light for eachwavelength λ of the visible wavelength range can be obtained. Then, theobtained diffraction efficiency η₁(λ) is averaged across the visiblewavelength range, and therefore an average diffraction efficiency ηacross visible wavelength can be obtained, which is an average value ofthe diffraction efficiency η₁(λ) of first-order diffracted light in thevisible wavelength range.

However, the expression (29) is a function not only for the wavelengthλ, but also for the grating height h. The grating height h is determineddepending on the blaze wavelength λ_(b). That is, the blaze wavelengthλ_(b) is equivalent to a diffraction efficiency η_(m)(λ) of 1 (i.e.,100%), thereby providing φ(λ_(b))−m=0 based on the expression (28). Thisexample is intended for the first-order diffracted light, and thereforeφ(λ_(b))=1 when m=1. When such a value is substituted into theexpression (29), and the expression (29) is rearranged,h=λ _(b) /{n ₁(λ_(b))−n ₂(λ_(b))}  (31)As for material, a refractive index n_(d) and an Abbe number ν_(d) ofwhich at a d line are given, and which has typical wavelengthdispersion, a refractive index n(λ) for each wavelength λ (μm) can becalculated based on the following Hertzberger's expressions (32)-(34):A(λ)=0.088927×λ²−1.294878+0.37349/(λ²−0.035)+0.005799/(λ²−0.035)²  (32)B(λ)=0.001255−0.007058×λ²+0.001071/(λ²−0.035)−0.000218/(λ²−0.035)²  (33)n(λ)=1+(n _(d)−1)×{1+B(λ)+(A(λ)/ν_(d))}  (34)

Thus, the blaze wavelength λ_(b) and the materials of the first andsecond optical members 10 and 11 (i.e., a refractive index n₁(λ_(d)) andan Abbe number ν_(d1) at a d line of the first optical member 10, and arefractive index n₂(λ_(d)) and an Abbe number ν_(d2) at a d line of thesecond optical member 11) are first determined. Next, a refractive indexn₁(λ_(b)) of the first optical member 10 and a refractive indexn₂(λ_(b)) of the second optical member 11 for the blaze wavelength areobtained based on the expressions (32)-(34), and then such values aresubstituted into the expression (31) to obtain the grating height h. Theobtained grating height h is substituted into the expression (29), andthe wavelength λ is changed in the visible wavelength range. Then, thediffraction efficiency η₁(λ) of first-order diffracted light for eachwavelength λ is obtained based on the expression (30). At this point,the refractive index n₁(λ) of the first optical member 10 and therefractive index n₂(λ) of the second optical member 11 for eachwavelength λ are obtained based on the expressions (32)-(34). Finally,the diffraction efficiency η₁(λ) of first-order diffracted light foreach wavelength λ is averaged across the visible wavelength range toobtain the average diffraction efficiency η across visible wavelength.

Further, the inter-material gradient M is obtained based on anexpression (35):M={n ₁(λ₂)−n ₂(λ₂)}/{n ₁(λ₁)−n ₁(λ₃)−n ₂(λ₁)+n ₂(λ₃)}  (35)

where “n₁(λ)” represents a refractive index of the first optical memberfor incident light having a wavelength λ; “n₂(λ)” represents arefractive index of the second optical member for the incident lighthaving the wavelength λ; “λ₁” is 0.486133 μm; “λ₂” is 0.587562 μm; and“λ₃” is 0.656273 μm. As described above, the refractive index n₁(λ) ofthe first optical member 10 and the refractive index n₂(λ) of the secondoptical member 11 for each of the wavelengths λ₁, λ₂, and λ₃ areobtained based on the expressions (32)-(34).

Thus, an average diffraction efficiency η(λ_(b), M) across visiblewavelength for a certain inter-material gradient M and the blazewavelength λ_(b) can be obtained.

The foregoing calculation is performed while changing the inter-materialgradient M (i.e., at least one of the refractive index n₁(λ_(d)) and theAbbe number ν_(d1) at the d line of the first optical member 10; and therefractive index n₂(λ_(d)) and the Abbe number ν_(d2) at the d line ofthe second optical member 11) and the blaze wavelength λ_(b). In such amanner, the average visible wavelength diffraction efficiencies η(λ_(b),M) for various inter-material gradients M and blaze wavelengths λ_(b)can be obtained. Specifically, the blaze wavelength λ_(b) is changed by0.001 μm within a range of 0.400 μm-0.700 μm. In addition, therefractive index n₁(λ_(d)) at the d line of the first optical member 10is fixed to 1.60000; the Abbe number ν_(d1) of the first optical member10 is fixed to 27.00; the refractive index n₂(λ_(d)) at the d line ofthe second optical member 11 is fixed to 1.65000. The Abbe number ν_(d2)of the second optical member 11 is changed to vary the inter-materialgradient M. The results are illustrated in FIG. 4.

As will be seen from FIG. 4, the average diffraction efficiency η acrossvisible wavelength can be improved within a range specified by anexpression (12):−6.30≦M≦−4.55  (12)

Specifically, selection of the suitable blaze wavelength λ_(b) allowsthe average diffraction efficiency η across visible wavelength to begreater than or equal to 98%, or further to be greater than or equal to99% in some cases. The maximum value of the diffraction efficiency forthe blaze wavelength λ_(b) is a constant value of 100%. Thus, theimprovement of the average diffraction efficiency η across visiblewavelength means reduction in deviation of the diffraction efficiencyfor each wavelength from 100%. That is, it means that the wavelengthdependency of the diffraction efficiency across the entire visiblewavelength range is reduced. The blaze wavelength λ_(b) is a designwavelength, and therefore can be relatively freely selected within,e.g., a range in which a desired optical performance can be realized inthe diffractive optical element 1. In particular, as in the diffractiveoptical element 1, if the diffraction efficiency is uniformly highacross the entire visible wavelength range, the high diffractionefficiency is realized for any wavelengths in the visible wavelengthrange. Thus, there is less limitation on the selection of the blazewavelength λ_(b). Consequently, as long as the first and second opticalmembers 10 and 11 are selected so that the inter-material gradient Mfalls within the range specified by the expression (12), the blazewavelength λ_(b) is adjusted as necessary to reduce the wavelengthdependency of the diffraction efficiency in the visible wavelengthrange.

Within a range specified by expressions (1)-(3) or (4)-(6), the averagediffraction efficiency η across visible wavelength can be furtherimproved. The ranges corresponding to the expressions (1)-(3) and(4)-(6) are illustrated in FIG. 5. Data in some examples and comparativeexamples is illustrated in Tables 1 and 2, and the diffractionefficiency in the visible wavelength range is illustrated in FIG. 6. Agraph of the average diffraction efficiency η across visible wavelengthbased on the inter-material gradient M and the blaze wavelength λ_(b) inFIG. 5 is the same as that in FIG. 4.0.400≦λ_(b)≦0.460  (1)M≧1339242229.625×λ_(b) ⁶−3467101052.6675×λ_(b) ⁵+3739417158.03949×λ_(b)⁴−2150706261.50666×λ_(b) ³+695699517.122797×λ_(b)²−120005677.292515×λ_(b)+8624042.63627238  (2)M≦−1332094191.9375×λ_(b) ⁶+3449257434.95906×λ_(b)⁵−3720886459.39374×λ_(b) ⁴+2140458094.5947×λ_(b)³−692516647.829495×λ_(b) ²+119479540.773725×λ_(b)−8587922.98149309  (3)0.560≦λ_(b)≦0.650  (4)M≧79855185.5390625×λ_(b) ⁶−291350087.799711×λ_(b)⁵+442815879.530274×λ_(b) ⁴−358873164.839002×λ_(b)³+163567486.506001×λ_(b) ²−39753252.4920047×λ_(b)+4024975.0978217  (5)M≦−82526017.6289062×λ_(b) ⁶+301239002.375121×λ_(b)⁵−458051447.988191×λ_(b) ⁴+371372898.921825×λ_(b)³−169325896.092434×λ_(b) ²+41165269.8970695×λ_(b)−4168933.51144255  (6)

TABLE 1 Average Diffraction First Optical Member Second Optical MemberEfficiency Abbe Abbe Blaze η across Refractive Number Refractive NumberGradient Wavelength Visible Material Index n_(d) ν_(d) Material Indexn_(d) ν_(d) M λ_(b) (μm) Wavelength Example 1-1 UV 1.60000 27.00Hypothetical 1.65000 45.62 −6.27 0.409/0.587 99.0% ∘ Curable Glass ResinExample 1-2 UV 1.60000 27.00 Hypothetical 1.65000 57.50 −4.580.447/0.632 99.0% ∘ Curable Glass Resin Example 1-3 UV 1.60000 27.00Hypothetical 1.65000 51.19 −5.25 0.432/0.607 99.3% Δ Curable Glass ResinExample 1-4 UV 1.60000 27.00 Hypothetical 1.65000 51.19 −5.250.449/0.569 99.0% ∘ Curable Glass Resin Example 1-5 UV 1.60000 27.00Hypothetical 1.65000 51.19 −5.25 0.420/0.641 99.0% ∘ Curable Glass ResinExample 1-6 Acrylate 1.606  26.00 Phosphate 1.65650 48.7  −5.14 0.60099.3% Δ UV Optical Curable Glass Resin Example 1-7 Acrylate 1.606  26.00K-VC78 1.66955 55.4  −5.66 0.588 99.2% Δ UV Manufactured Curable bySumita Resin Optical Glass Inc. Example 1-8 SiO₂TI₂O 1.718  19.3  K-VC891.81000 41.0  −5.25 0.600 99.3% Δ Sol-Gel Manufactured Glass by SumitaOptical Glass Inc. Comparative UV 1.60000 27.00 Hypothetical 1.6500051.19 −5.25 0.410/0.678 98.0% x Example 1-1 Curable Glass ResinComparative UV 1.60000 27.00 Hypothetical 1.65000 51.19 −5.25 0.49998.2% x Example 1-2 Curable Glass Resin Comparative UV 1.60000 27.00Hypothetical 1.65000 63.17 −4.19 0.476/0.607 98.0% x Example 1-3 CurableGlass Resin Comparative UV 1.60000 27.00 Hypothetical 1.65000 41.53−7.61 0.375/0.607 98.0% x Example 1-4 Curable Glass Resin

TABLE 2 Average Diffraction First Optical Member Second Optical MemberEfficiency Abbe Abbe Blaze η across Refractive Number Refractive NumberGradient Wavelength Visible Material Index n_(d) ν_(d) Material Indexn_(d) ν_(d) M λ_(b) (μm) Wavelength Example UV 1.60000 27.00Hypothetical 1.65000 47.37 −5.92 0.417/0.592 99.15% □ 1-9  Curable GlassResin Example UV 1.60000 27.00 Hypothetical 1.65000 55.58 −4.750.444/0.623 99.15% □ 1-10 Curable Glass Resin Example UV 1.60000 27.00Hypothetical 1.65000 53.72 −4.94 0.636 99.16% □ 1-11 Curable Glass ResinExample UV 1.60000 27.00 Hypothetical 1.65000 49.50 −5.50 0.577 99.15% □1-12 Curable Glass Resin Example UV 1.60000 27.00 Hypothetical 1.6500053.99 −4.91 0.448 99.16% □ 1-13 Curable Glass Resin Example UV 1.6000027.00 Hypothetical 1.65000 47.79 −5.80 0.415 99.15% □ 1-14 Curable GlassResin Example UV 1.60000 27.00 Hypothetical 1.65000 47.95 −5.770.420/0.595 99.20% Δ 1-15 Curable Glass Resin Example UV 1.60000 27.00Hypothetical 1.65000 54.66 −4.84 0.442/0.620 99.20% Δ 1-16 Curable GlassResin Example UV 1.60000 27.00 Hypothetical 1.65000 53.18 −5.00 0.63099.21% Δ 1-17 Curable Glass Resin Example UV 1.60000 27.00 Hypothetical1.65000 49.63 −5.48 0.583 99.21% Δ 1-18 Curable Glass Resin Example UV1.60000 27.00 Hypothetical 1.65000 53.63 −4.95 0.445 99.21% Δ 1-19Curable Glass Resin Example UV 1.60000 27.00 Hypothetical 1.65000 48.32−5.70 0.419 99.21% Δ 1-20 Curable Glass Resin

That is, a relationship with the blaze wavelength λ_(b) is considered inaddition to the inter-material gradient M, thereby further improving theaverage diffraction efficiency η across visible wavelength.Specifically, as will be seen from FIG. 5, the average diffractionefficiency η across visible wavelength can be greater than or equal to99%. In other words, the inter-material gradient M and the blazewavelength λ_(b) are selected so that the expressions (2) and (3) aresatisfied in a range in which the blaze wavelength λ_(b) satisfies theexpression (1). Alternatively, the inter-material gradient M and theblaze wavelength λ_(b) are selected so that the expressions (5) and (6)are satisfied in a range in which the blaze wavelength λ_(b) satisfiesthe expression (4). In such a manner, the average diffraction efficiencyη across visible wavelength can be further improved. As will be seenfrom FIG. 6, the deviation of the diffraction efficiency for eachwavelength from 100% is reduced by improving the average diffractionefficiency η across visible wavelength. Consequently, the wavelengthdependency of the diffraction efficiency across the entire visiblewavelength range can be further reduced. In addition, a lessinter-material gradient M (i.e., a smaller absolute value of theinter-material gradient M) results in more degradation of thediffraction efficiency on a shorter wavelength side, whereas a greaterinter-material gradient M (i.e., a larger absolute value of theinter-material gradient M) results in more degradation of thediffraction efficiency on a longer wavelength side.

The expressions (1) and (4) provide a rough estimate of the blazewavelength λ_(b), and even the blaze wavelength λ_(b) falling withinsuch an estimate may not satisfy the expressions (2) and (3), or (5) and(6). That is, it is required that the blaze wavelength λ_(b) satisfiesthe expression (1) or (4), as well as the expressions (2) and (3), or(5) and (6).

Further, within a range specified by expressions (7)-(9) or (10)-(12),the average diffraction efficiency η across visible wavelength isfurther improved. The ranges corresponding to the expressions (7)-(9)and (10)-(12) are illustrated in FIG. 7. A graph of the averagediffraction efficiency η across visible wavelength based on theinter-material gradient M and the blaze wavelength λ_(b) in FIG. 7 isthe same as that in FIG. 4.0.414≦λ_(b)≦0.450  (7)M≧8640558390×λ_(b) ⁶−22380686760.9125×λ_(b) ⁵+24152666332.3616×λ_(b)⁴−13900381865.2731×λ_(b) ³+4499685153.88293×λ_(b)²−776796861.97245×λ_(b)+55871807.7607997  (8)M≦−10194570607.5λ_(b) ⁶+26421929920.0925×λ_(b) ⁵−28531440313.7911×λ_(b)⁴+16430708380.9751×λ_(b) ³−5322137506.01958×λ_(b)²+919367999.430877×λ_(b)−66169280.3167743  (9)0.576≦λ_(b)≦0.638  (10)M≧414967120.90625×λ_(b) ⁶−1512185155.554×λ_(b) ⁵+2295832124.5403×λ_(b)⁴−1858788442.14493×λ_(b) ³+846446107.028953×λ_(b)²−205553837.085777×λ_(b)+20796969.7061844  (11)M≦−415113085.03125×λ_(b) ⁶+1512854887.23366×λ_(b)⁵−2297046202.65628×λ_(b) ⁴+1859918525.18878×λ_(b)³−847020476.777119×λ_(b) ²+205705688.874443×λ_(b)−20813340.0724713  (12)

Within the range satisfying the expressions (7)-(9) or (10)-(12), theaverage diffraction efficiency η across visible wavelength can begreater than or equal to 99.15%. Specifically, the inter-materialgradient M and the blaze wavelength λ_(b) are selected so that theexpressions (8) and (9) are satisfied within a range in which the blazewavelength λ_(b) satisfies the expression (7). Alternatively, theinter-material gradient M and the blaze wavelength λ_(b) are selected sothat the expressions (11) and (12) are satisfied within a range in whichthe blaze wavelength λ_(b) satisfies the expression (10). In such amanner, the average diffraction efficiency η across visible wavelengthcan be further improved. The improvement of the average diffractionefficiency η across visible wavelength further reduces the wavelengthdependency of the diffraction efficiency across the entire visiblewavelength range. Note that the expressions (7) and (10) provide a roughestimate of the blaze wavelength λ_(b), and even the blaze wavelengthλ_(b) falling within such an estimate may not satisfy the expressions(8) and (9), or (11) and (12). That is, it is required that the blazewavelength λ_(b) satisfies the expression (7) or (10), as well as theexpressions (8) and (9), or (11) and (12).

Further, within a range specified by expressions (13)-(15) or (16)-(18),the average diffraction efficiency η across visible wavelength can befurther improved. The ranges corresponding to the expressions (13)-(15)and (16)-(18) are illustrated in FIG. 8. A graph of the averagediffraction efficiency across visible wavelength based on theinter-material gradient M and the blaze wavelength λ_(b) in FIG. 8 isthe same as that in FIG. 4.0.417≦λ_(b)≦0.447  (13)M≧30852412488×λ_(b) ⁶−79922201016.868×λ_(b) ⁵+86260883694.3531×λ_(b)⁴−49652199810.7073×λ_(b)+16075519544.8254×λ_(b)²−2775681903.96431×λ_(b)+199683678.257006  (14)M≦−30584648780×λ_(b) ⁶+79226520575.83×λ_(b) ⁵−85507821323.3087×λ_(b)⁴+49217462978.353×λ_(b) ³−15934356981.3252×λ_(b)²+2751237292.99331×λ_(b)−197920088.494362  (15)0.581≦λ_(b)≦0.632  (16)M≧1306900213.875×λ_(b) ⁶−4761329435.24312×λ_(b) ⁵+7227224601.18296×λ_(b)⁴−5850360432.19395×λ_(b) ³+2663701689.21584×λ_(b)²−646780698.688165×λ_(b)+65431590.8897632  (17)M≦−1286672013.625×λ_(b) ⁶+4687809955.26×λ_(b) ⁵−7115891461.56486×λ_(b)⁴+5760442316.00334×λ_(b) ³−2622849972.06735×λ_(b)²+636881343.787066×λ_(b)−64431960.7758904  (18)

Within the range satisfying the expressions (13)-(15) or (16)-(18), theaverage diffraction efficiency η across visible wavelength can begreater than or equal to 99.20%. Specifically, the inter-materialgradient M and the blaze wavelength λ_(b) are selected so that theexpressions (14) and (15) are satisfied within a range in which theblaze wavelength λ_(b) satisfies the expression (13). Alternatively, theinter-material gradient M and the blaze wavelength λ_(b) are selected sothat the expressions (17) and (18) are satisfied within a range in whichthe blaze wavelength λ_(b) satisfies the expression (16). In such amanner, the average diffraction efficiency η across visible wavelengthcan be further improved. The improvement of the average diffractionefficiency η across visible wavelength further reduces the wavelengthdependency of the diffraction efficiency across the entire visiblewavelength range. Note that the expressions (13) and (16) provide arough estimate of the blaze wavelength λ_(b), and even the blazewavelength λ_(b) falling within such an estimate may not satisfy theexpressions (14) and (15), or (17) and (18). That is, it is requiredthat the blaze wavelength λ_(b) satisfies the expression (13) or (16),as well as the expressions (14) and (15), or (17) and (18).

When satisfying expressions (19)-(23) within each of ranges of the blazewavelength λ_(b) in (i)-(iii), the average diffraction efficiency ηacross visible wavelength can be improved. The ranges corresponding tothe expressions (19)-(23) are illustrated in FIG. 9. Data in someexamples and comparative examples is illustrated in Table 3, and thediffraction efficiency in the visible wavelength range is illustrated inFIG. 10. A graph of the average diffraction efficiency η across visiblewavelength based on the inter-material gradient M and the blazewavelength λ_(b) in FIG. 9 is the same as that in FIG. 4.

(i) When 0.402≦λ_(b)<0.423,M≧−5.67  (19)M≦−2059169.7421875×λ_(b) ⁶+5816357.49453125×λ_(b)⁵−6788300.15627441×λ_(b) ⁴+4193835.50001671×λ_(b)³−1448014.62341355×λ_(b) ²+265253.074154754×λ_(b)−20174.8108751328  (20)

(ii) When 0.423≦λ_(b)<0.664,−5.67≦M≦−4.70  (21)

(iii) When 0.664≦λ_(b)≦0.695,M≧−1737676.76663208×λ_(b) ⁶+6606429.15555359×λ_(b)⁵−10426872.1241855×λ_(b) ⁴+8742622.74935995×λ_(b)³−4106195.43419261×λ_(b) ²+1024012.6733048×λ_(b)−105911.832822947  (22)M≦−4.70  (23)

TABLE 3 Average Diffraction First Optical Member Second Optical MemberEfficiency Abbe Abbe Blaze η across Refractive Number Refractive NumberGradient Wavelength Visible Material Index n_(d) ν_(d) Material Indexn_(d) ν_(d) M λ_(b) (μm) Wavelength Example 2-1 UV 1.60000 27.00Hypothetical 1.65000 48.49 −5.67 0.488 98.0% ▾ Curable Glass ResinExample 2-2 UV 1.60000 27.00 Hypothetical 1.65000 56.11 −4.70 0.51498.0% ▾ Curable Glass Resin Example 2-3 UV 1.60000 27.00 Hypothetical1.65000 51.19 −5.25 0.410/0.678 98.0% ▾ Curable Glass Resin Example 2-4UV 1.60000 27.00 Hypothetical 1.65000 51.19 −5.25 0.499 98.2% ▾ CurableGlass Resin Example 2-5 UV 1.60000 27.00 Hypothetical 1.65000 48.49−5.67 0.402/0.664 98.0% ▾ Curable Glass Resin Example 1-6 Acrylate1.606  26.00 Phosphate 1.65650 48.7  −5.14 0.600 99.3% ▾ UV OpticalGlass Curable Resin Example 1-7 Acrylate 1.606  26.00 K-VC78 1.6695555.4  −5.66 0.588 99.2% ▾ UV Manufactured Curable by Sumita ResinOptical Glass Inc. Example 1-8 SiO₂TI₂O 1.718  19.3  K-VC89 1.8100041.0  −5.25 0.600 99.3% ▾ Sol-Gel Manufactured Glass by Sumita OpticalGlass Inc. Comparative UV 1.60000 27.00 Hypothetical 1.65000 48.49 −6.920.488 97.0% x Example 2-1 Curable Glass Resin Comparative UV 1.6000027.00 Hypothetical 1.65000 48.49 −4.13 0.514 97.0% x Example 2-2 CurableGlass Resin Comparative UV 1.60000 27.00 Hypothetical 1.65000 51.19−5.25 0.405/0.702 97.0% x Example 2-3 Curable Glass Resin

As will be seen from FIG. 9, within all of the ranges satisfying theexpressions (19)-(23), the average diffraction efficiency η acrossvisible wavelength is greater than or equal to 98%. Such ranges coversthe substantially entire visible wavelength range. Thus, if the firstand second optical members 10 and 11 are selected so that theexpressions (19)-(23) are satisfied, the average diffraction efficiencyη across visible wavelength can be greater than or equal to 98% for anyblaze wavelengths λ_(b) in the visible wavelength range. That is, theblaze wavelength λ_(b) and the first and second optical members 10 and11 can be more flexibly selected while the wavelength dependency of thediffraction efficiency across the entire visible wavelength range can bereduced.

Various combinations of the first and second optical members 10 and 11,which are selected so as to have the same inter-material gradient M areillustrated in Table 4 and FIG. 11. A vertical axis of a graph in FIG.11 is a reference refractive index (n(λ_(d))), and a horizontal axis isa principal dispersion (n(λ_(F))−n(λ_(C))).

TABLE 4 First Second Refractive Optical Refractive Abbe OpticalRefractive Abbe Gradient Index Member Index n_(d) Number ν_(d) MemberIndex n_(d) Number ν_(d) M Difference Example SiO₂/TI₂O 1.50334548.31435 BSL7 1.51633  64.1   −5.495 0.012985 3-1 Example SiO₂/TI₂O1.528818 38.87719 BAL5 1.547393 53.5507 −5.495 0.018575 3-2 ExampleSiO₂/TI₂O 1.532572 37.84758 BAL50 1.559625 61.1727 −5.495 0.027053 3-3Example SiO₂/TI₂O 1.5375  36.59582 BAL22 1.568729 63.1624 −5.4950.031229 3-4 Example SiO₂/TI₂O 1.548684 34.1104  BAL42 1.58313  59.4  −5.495 0.034446 3-5 Example SiO₂/TI₂O 1.564346 31.27741 BSM7 1.60729159.3756 −5.495 0.042945 3-6 Example SiO₂/TI₂O 1.585108 28.35037 BSM811.64   60.1   −5.495 0.054892 3-7 Example SiO₂/TI₂O 1.598666 26.80608LAL11 1.658293 57.3326 −5.495 0.059627 3-8 Example SiO₂/TI₂O 1.61281925.4257  LAL12 1.6779  55.3   −5.495 0.065081 3-9 Example SiO₂/TI₂O1.646697 22.82156 LAL18 1.72916  54.7   −5.495 0.082463  3-10 ExampleSiO₂/TI₂O 1.665617 21.67982 YGH51 1.755   52.3   −5.495 0.089383  3-11Example SiO₂/TI₂O 1.699478 20.0224  LAH67 1.794997 45.294  −5.4950.095519  3-12 Example SiO₂/TI₂O 1.72959  18.85305 LAH55 1.83481  42.7  −5.495 0.10522   3-13 Example SiO₂/TI₂O 1.769819 17.60496 LAH75 1.87399635.286  −5.495 0.104177  3-14

The first optical member 10 is SiO₂—Tl₂O glass formed by mixing SiO₂ andTl₂O together, and a mixing ratio of such components is changed torealize various refractive indexes n₁(λ_(d)) and Abbe numbers ν_(d1).The second optical member 11 is optical glass manufactured by OharaInc., and is illustrated with model numbers in Table 2. In any of thecombinations of the first and second optical members 10 and 11, theinter-material gradient M is −5.495. That is, in FIG. 11, a lineconnecting between the first optical member 10 and the second opticalmember 11 in each of the combinations is parallel to other lines.

In each of the combinations of the first and second optical members 10and 11, the blaze wavelength λ_(b) is set to 0.605 μm, and then thegrating height h is obtained based on the expressions (31)-(34). Theobtained grating height h is used to obtain the average diffractionefficiency η across visible wavelength as described above. That is, thegrating height h is substituted into the expression (29), and thewavelength λ is changed in the visible wavelength range. Then, thediffraction efficiency η₁(λ) of first-order diffracted light for eachwavelength λ is obtained based on the expression (30). Finally, thediffraction efficiency η₁(λ) of first-order diffracted light for eachwavelength λ is averaged across the visible wavelength range to obtainthe average diffraction efficiency η across visible wavelength. Table 5illustrates the average diffraction efficiency η across visiblewavelength and diffraction efficiencies η₁(λ) for some representativewavelengths in each of the combinations corresponding to Table 4.

TABLE 5 Diffraction Efficiency (%) Average Diffraction Blaze EfficiencyWave- Grating η across length Height h Visible 0.400 0.450 0.500 0.5500.600 0.650 0.700 λ_(b) (μm) (μm) Wavelength μm μm μm μm μm μm μmExample 0.605 45.9 99.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1 3-1 Example0.605 32.1 99.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1 3-2 Example 0.60522.0 99.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1 3-3 Example 0.605 19.199.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1 3-4 Example 0.605 17.3 99.397.5 99.4 98.8 99.4 100.0 99.4 97.1 3-5 Example 0.605 13.9 99.3 97.599.4 98.8 99.4 100.0 99.4 97.1 3-6 Example 0.605 10.9 99.3 97.5 99.498.8 99.4 100.0 99.4 97.1 3-7 Example 0.605 10.0 99.3 97.5 99.4 98.899.4 100.0 99.4 97.1 3-8 Example 0.605  9.2 99.3 97.5 99.4 98.8 99.4100.0 99.4 97.1 3-9 Example 0.605  7.2 99.3 97.5 99.4 98.8 99.4 100.099.4 97.1  3-10 Example 0.605  6.7 99.3 97.5 99.4 98.8 99.4 100.0 99.497.1  3-11 Example 0.605  6.2 99.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1 3-12 Example 0.605  5.7 99.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1  3-13Example 0.605  5.7 99.3 97.5 99.4 98.8 99.4 100.0 99.4 97.1  3-14

As will be seen from Table 5, an identical pair of the inter-materialgradient M and the blaze wavelength λ_(b) produces constant diffractionefficiency η₁(λ) for each wavelength and constant average diffractionefficiency η across visible wavelength. The graphs of FIGS. 4, 5, and7-9 illustrate the results when the inter-material gradient M is changedby changing the Abbe number ν_(d2) of the second optical member 11 inthe state in which the refractive index n₁(λ_(d)) and the Abbe numberν_(d1) at the d line of the first optical member 10, and the refractiveindex n₂(λ_(d)) at the d line of the second optical member 11 are fixedto the predetermined values. However, an identical inter-materialgradient M produces constant average diffraction efficiency η acrossvisible wavelength for the certain blaze wavelength λ_(b). Thus, even ifthe refractive index n₁(λ_(d)) and the Abbe number ν_(d1) at the d lineof the first optical member 10, and the refractive index n₂(λ_(d)) atthe d line of the second optical member 11 are different, resultssimilar to those in FIGS. 4, 5, and 7-9 may be obtained. Thus, theexpressions (1)-(23) are satisfied regardless of the refractive indexn₁(λ_(d)) and the Abbe number ν_(d1) at the d line of the first opticalmember 10, and the refractive index n₂(λ_(d)) and the Abbe number ν_(d2)at the d line of the second optical member 11.

Next, a relationship between the grating height h (μm) and theabsorption coefficient α (mm⁻¹) will be described.

It is assumed that the first optical member 10 is made of opticalmaterial having a complex refractive index, and the second opticalmember 11 is made of optical material having no absorption. Asillustrated in FIG. 12, a grating pitch P of the diffraction grating 13is 150 μm, and the blaze wavelength λ_(b) is at the d line (0.587562μm). A simulation was performed by a rigorous coupled-wave analysis(RCWA) method while changing the grating height h within a range of 1-25μm, and changing the complex refractive index. In this way, thediffraction efficiency of first-order diffracted light for the blazewavelength λ_(b) was obtained. The results are illustrated in FIG. 13.

As will be seen from FIG. 13, within a range satisfying expressions (24)and (25), the diffraction efficiency for the blaze wavelength λ_(b) canbe greater than 85%:α≧0.04  (24)h≦263.18×α^(−0.9454)  (25)

Thus, even if the absorption coefficient is greater than or equal to0.04 mm⁻¹, i.e., the optical material which is not optically transparentis used, the high diffraction efficiency can be realized as long as theexpression (25) is satisfied. Thus, such material may be employed as thefirst optical member 10. Consequently, the range of the first opticalmember 10 to be selected can be expanded.

Preferably, within a range satisfying an expression (26) in addition tothe expression (25), the diffraction efficiency for the blaze wavelengthλ_(b) can be greater than 90%:h≦166.36×α^(−0.9444)  (26)

More preferably, within a range satisfying an expression (27) inaddition to the expression (25), the diffraction efficiency for theblaze wavelength λ_(b) can be greater than 95%:h≦67.349×α^(−0.898)  (27)

As described above, the expression (26) or (27) is satisfied, andtherefore the optical material which is not optically transparent isemployed as the first optical member 10 while maintaining the highdiffraction efficiency. That is, both of the maintenance of the highdiffraction efficiency and the expansion of the range of the materialselection can be realized.

Other Embodiments

The present disclosure may have the following configurations in theforegoing embodiment.

That is, in the foregoing embodiment, the diffractive optical element 1is employed in the interchangeable lens 200, but the present disclosureis not limited to such a configuration. The diffractive optical element1 may be employed as a lens element inside the camera 100. In addition,the present disclosure is not limited to the diffractive optical element1 serving as the lens, and the diffractive optical element 1 may beapplied for purposes other than the foregoing purpose.

In the foregoing embodiment, the first optical member 10 is made ofresin material, and the second optical member 11 is made of glassmaterial. However, the present disclosure is not limited to such aconfiguration. The first optical member 10 may be made of glassmaterial, and the second optical member 11 may be made of resinmaterial. Alternatively, both of the first and second optical members 10and 11 may be made of glass material or resin material.

The first and second optical members 10 and 11 may be made of materialformed by mixing inorganic particulates (so-called “nanocomposites”)with resin. The inorganic particulates can adjust the refractive indexand the Abbe number of the optical member.

The diffractive optical element 1 may satisfy at least one group of theexpressions (1)-(3), (4)-(6), or (19)-(23). In addition to theexpressions, the diffractive optical element 1 may preferably satisfythe expressions (24) and (25).

If there are various grating heights as illustrated in FIG. 14, adistance between an intersection point of a line parallel to the opticalaxis, and one of the adjacent inclined surfaces; and an intersectionpoint of the line and the other inclined surface is the grating heighth.

The refractive index n(λ) for each wavelength λ is calculated based onthe Hertzberger's expressions, but the present disclosure is not limitedto such a configuration. The refractive index n(λ) may be an actualmeasured value, or may be a value calculated by a publicly-known method.

The foregoing embodiments have been set forth merely for purposes ofpreferred examples in nature, and are not intended to limit the scope,applications, and use of the present disclosure.

As described above, the present disclosure is useful for the diffractiveoptical element in which the two optical members are stacked, and thediffraction grating is formed at the interface between the two opticalmembers. In particular, the present disclosure is useful for thediffractive optical element intended for light in the visible wavelengthrange.

What is claimed is:
 1. A diffractive optical element, comprising: firstand second optical members which are stacked, and which have adiffraction grating formed at an interface between the first and secondoptical members, wherein expressions (1)-(3) or (4)-(6) are satisfied:0.400≦λ_(b)≦0.460  (1)M≧1339242229.625×λ_(b) ⁶−3467101052.6675×λ_(b) ⁵+3739417158.03949×λ_(b)⁴−2150706261.50666×λ_(b) ³+695699517.122797×λ_(b)²−120005677.292515×λ_(b)+8624042.63627238  (2)M≦−1332094191.9375×λ_(b) ⁶+3449257434.95906×λ_(b)⁵−3720886459.39374×λ_(b) ⁴+2140458094.5947×λ_(b)³−692516647.829495×λ_(b) ²+119479540.773725×λ_(b)−8587922.98149309  (3)0.560≦λ_(b)≦0.650  (4)M≧79855185.5390625×λ_(b) ⁶−291350087.799711×λ_(b)⁵+442815879.530274×λ_(b) ⁴−358873164.839002×λ_(b)³+163567486.506001×λ_(b) ²−39753252.4920047×λ_(b)+4024975.0978217  (5)M≦−82526017.6289062×λ_(b) ⁶+301239002.375121×λ_(b)⁵−458051447.988191×λ_(b) ⁴+371372898.921825×λ_(b)³−169325896.092434×λ_(b) ²+41165269.8970695×λ_(b)−4168933.51144255  (6)where “λ_(b)” is a blaze wavelength (μm);M={n₁(λ₂)−n₂(λ₂)}/{n₁(λ₁)−n₁(λ₃)−n₂(λ₁)+n₂(λ₃)}; “n₁(λ)” is a refractiveindex of the first optical member for incident light having a wavelengthλ; “n₂(λ)” is a refractive index of the second optical member for theincident light having the wavelength λ; “λ₁” is 0.486133 μm; “λ₂” is0.587562 μm; and “λ₃” is 0.656273 μm.
 2. The diffractive optical elementof claim 1, wherein expressions (7)-(9) or (10)-(12) are satisfied:0.414≦λ_(b)≦0.450  (7)M≧8640558390×λ_(b) ⁶−22380686760.9125×λ_(b) ⁵+24152666332.3616×λ_(b)⁴−13900381865.2731×λ_(b) ³+4499685153.88293×λ_(b)²−776796861.97245×λ_(b)+55871807.7607997  (8)M≦−10194570607.5×λ_(b) ⁶+26421929920.0925×λ_(b) ⁵−28531440313.7911×λ_(b)⁴+16430708380.9751×λ_(b) ³−5322137506.01958×λ_(b)²+919367999.430877×λ_(b)−66169280.3167743  (9)0.576≦λ_(b)≦0.638  (10)M≧414967120.90625×λ_(b) ⁶−1512185155.554×λ_(b) ⁵+2295832124.5403×λ_(b)⁴−1858788442.14493×λ_(b) ³+846446107.028953×λ_(b)²−205553837.085777λ_(b)×20796969.7061844  (11)M≦−415113085.03125×λ_(b) ⁶+1512854887.23366×λ_(b)⁵−2297046202.65628×λ_(b) ⁴+1859918525.18878×λ_(b)³−847020476.777119×λ_(b)²+205705688.874443×λ_(b)−20813340.0724713  (12).
 3. The diffractiveoptical element of claim 1, wherein expressions (13)-(15) or (16)-(18)are satisfied:0.417≦λ_(b)≦0.447  (13)M≧30852412488×λ_(b) ⁶−79922201016.868×λ_(b) ⁵+86260883694.3531×λ_(b)⁴−49652199810.7073×λ_(b) ³+16075519544.8254×λ_(b)²−2775681903.96431×λ_(b)+199683678.257006  (14)M≦−30584648780×λ_(b) ⁶+79226520575.83×λ_(b) ⁵−85507821323.3087×λ_(b)⁴+49217462978.353×λ_(b) ³−15934356981.3252×λ_(b)²+2751237292.99331×λ_(b)−197920088.494362  (15)0.581≦λ_(b)≦0.632  (16)M≧1306900213.875×λ_(b) ⁶−4761329435.24312×λ_(b) ⁵+7227224601.18296×λ_(b)⁴−5850360432.19395×λ_(b) ³+2663701689.21584×λ_(b)²−646780698.688165×λ_(b)+65431590.8897632  (17)M≦−1286672013.625×λ_(b) ⁶+4687809955.26×λ_(b) ⁵−7115891461.56486×λ_(b)⁴+5760442316.00334×λ_(b) ³−2622849972.06735×λ_(b)²+636881343.787066×λ_(b)−64431960.7758904  (18).
 4. The diffractiveoptical element of claim 1, wherein an absorption coefficient α (mm⁻¹)of the first optical member and a grating height h (μm) of thediffraction grating satisfy expressions (24) and (25):α≧0.04  (24)h≦263.18×α^(−0.9454)  (25).
 5. An optical device, comprising: an opticalimaging system for focusing light bundles on a predetermined surface,wherein the optical imaging system has the diffractive optical elementof claim
 1. 6. A diffractive optical member, comprising: first andsecond optical members which are stacked, and which have a diffractiongrating formed at an interface between the first and second opticalmembers, wherein expressions (19)-(23) are satisfied depending on ablaze wavelength (μm): (i) when 0.402≦λ_(b)<0.423,M≧−5.67  (19)M≦−2059169.7421875×λ_(b) ⁶+5816357.49453125×λ_(b)⁵−6788300.15627441×λ_(b) ⁴+4193835.50001671×λ_(b)³−1448014.62341355×λ_(b) ²+265253.074154754×λ_(b)−20174.8108751328  (20)(ii) when 0.423≦λ_(b)<0.664,−5.67≦M≦−4.70  (21) (iii) when 0.664≦λ_(b)≦0.695,M≧−1737676.76663208×λ_(b) ⁶+6606429.15555359×λ_(b)⁵−10426872.1241855×λ_(b) ⁴+8742622.74935995×λ_(b)³−4106195.43419261×λ_(b) ²+1024012.6733048×λ_(b)−105911.832822947  (22)M≦−4.70  (23) where M={n₁(λ₂)−n₂(λ₂)}/{n₁(λ₁)−n₁(λ₃)−n₂(λ₁)+n₂(λ₃)};“n₁(λ)” is a refractive index of the first optical member for incidentlight having a wavelength λ; “n₂(λ)” is a refractive index of the secondoptical member for the incident light having the wavelength λ; “λ₁” is0.486133 μm; “λ₂” is 0.587562 μm; and “λ₃” is 0.656273 μm.
 7. Thediffractive optical element of claim 6, wherein an absorptioncoefficient α (mm⁻¹) of the first optical member and a grating height h(μm) of the diffraction grating satisfy expressions (24) and (25):α≧0.04  (24)h≦263.18×α^(−0.9454)  (25).